1. Sequences in GeoGebra
Sequences
MSP SI 2007
Sequences

2. Sequences What is a sequence? An ordered list of objects (or events)
Like a set, it contains members
(called elements or terms) and the
number of terms is called the length.
MSP SI 2007
Sequences

3. Workshop Objectives
You will be able to identify various sequences and use GeoGebra to:
Graphically represent sequences
Use the sequence command to create lists of objects
Use the element command to find
the nth term of a sequence
Use the segment command to
create line designs
MSP SI 2007
Sequences

4. 21 28 Number Patterns 11, 22, 33, 44, 55, ___, ___ 66 77
Find the next two terms of each sequence. Describe how you found each term.
11, 22, 33, 44, 55, ___, ___ 66 77 21 28
0, 1, 3, 6, 10, 15, ___, ___ 14 13
5, 8, 7, 10, 9, 12, 11, __,__
MSP SI 2007
Sequences
Slide Courtesy of Guy Barmoha

5. Sequences
Examples
Sequence
Notation
MSP SI 2007
Sequences

6. Arithmetic Sequences
Sequence of numbers where any 2 successive members have a common difference
Example:
( 0, 1, 2, 3, 4 )
MSP SI 2007
Sequences

7. Arithmetic Sequences
Sequence of numbers where any 2 successive members have a common difference
Example:
( 0, 3, 6, 9, 12 )
MSP SI 2007
Sequences

8. What would these sequences look like if we graphed them?X Y 1 3 2 6 9 4 12
MSP SI 2007
Sequences

9. What would these sequences look like if we graphed them?X Y 1 4 2 7 3 10 13
A line?
Possibly, but we need to check
it out! GeoGebra will help us.
MSP SI 2007
Sequences

10. What would these sequences look like if we graphed them?X Y 1 4 2 7 3 10 13
seq_line1.ggb
MSP SI 2007
Sequences

11. Sequences X Y 1 4 2 7 3 10 13 Common difference = 1 Common
Yes, this is a linear sequence!
How would we find the equation
of the line without graphing? X Y 1 4 2 7 3 10 13
y = m x + b
Common
difference = 1
Common
difference = 3
Slope= change y = 3
change x 1
y = 3 x + ?
y = 3 x + 1
MSP SI 2007
Sequences

12. Number Sequences What is the 7th term of this sequence?
Value 1 2 3 4 5 6 7 …
200 ? 7 10 13 16 19 22
What is the 7th term of this sequence?
What is the 200th term of this sequence?
MSP SI 2007
Sequences
Slide Courtesy of Guy Barmoha

13. Number Sequences 22 What is the 7th term of this sequence?
Value 1 2 3 4 5 6 7 …
200 ? 7 10 13 16 19 22 22
What is the 7th term of this sequence?
What is the 200th term of this sequence?
seq_line2.ggb
MSP SI 2007
Sequences

14. Sequences What equation is this? Slope-Intercept Form .
To find the nth term algebraically, use
an = a1 + (n-1) d
a1 = initial term, d = common difference .
Term
Value 1 2 3 4 5 6 7 …
200 7 10 13 16 19 22 … ?
What equation is this?
Slope-Intercept Form
y = 3x + 1
y = 3(200) + 1
y = 601
MSP SI 2007
Sequences

15. Sequences: GeoGebra Review
To create a list of objects:
Use sequence command:
Sequence[expression e, variable i, number a, number b]
To find the nth element in a list:
Use element command:
Element[List L, number n]
MSP SI 2007
Sequences

16. Sequences: Segments in GeoGebra
Slide background resembles Bezier curve
Dr. Pierre Bezier ( )
Engineer for French automaker
“Best fit” curve for manufacturing
Used in computer graphics
He used 4 points; We’ll use 3.
MSP SI 2007
Sequences
seq_line_art1.ggb

17. Segment Sequences Markus’ line art tool seq_line_art2.ggb MSP SI 2007

18. Sequences of Segments on a Circle
seq_circle_segments1.ggb
seq_circle_segments3.ggb
MSP SI 2007
Sequences

19. Sequences
SSS: MA.D.1.3.1, MA.D.2.4.1
All files will be posted on tiki at
Contact me at
Special thanks to Dr. Markus Hohenwarter
and Guy Barmoha, MST.
MSP SI 2007
Sequences